What is on the other side of the universe?
[Note: This is an astronomer's answer. There are numerous answers in series here, so if this one is too long, technical, or you just don't like it, see the numerous other answers beneath it!]
It depends on what you mean: 1) just farther than we can currently see in our observable universe or 2) outside of our Universe.
1) Very, very far away, farther than we can currently observe:
To the best of our current observations and theory, the Universe on the largest scales is homogeneous (i.e. 'smooth', or of similar density, composition, etc.) and isotropic (it looks the same in every direction). So, no matter where you are within our Universe, it should be about the same. That's the short answer.
Let me point out that our Universe has a finite and well-determined age; recent measurements put it at a little over 13 billion years (roughly 3 times the age of the solar system/Earth). There is a limit to how far away we can see--13 billion light-years--because the universe is only 13 billion years old, and light from farther away hasn't had time to get to us yet. This DOES NOT mean that the Universe is only 13 billion light-years in radius, and we are at the center of it; it is only our observable universe that is that size. As time passes, the size of our observable universe increases at the speed of light.
The actual size of our Universe is much larger; we just can't see it. So, to an observer farther than 13.4 billion light-years from us, outside our observable universe, things probably look about the same as they do here, but we won't know for sure until enough time passes for light (and gravity waves, neutrinos, whatever) arrive from there for us to observe.
Note that is is an assumption--that everywhere is about the same as it is here, and we're not at the center of the universe*(see below for why astronomers think this). This assumption is true for the amount of the universe we can observe, so most astronomers assume that it is true in general.
Expansion of the universe
How do we know we're not at the center of the universe? We observe the light from distant galaxies to be redshifted, which means that the galaxy is moving away from us very quickly. (Look up the Doppler effect; we hear the same effect from a moving sound source, such as a police car siren getting lower in pitch when the police car is moving away from us.)
Light from almost every galaxy, except those nearest to us (Andromeda, the Virgo cluster) is redshifted, meaning that everything is moving away from us, except for a few nearby galaxies. We can conclude that either: a) we are at the center of the universe, or b) space itself is expanding, and every galaxy sees most other galaxies moving away from it! We think it is b), that space is expanding. You can understand this in two dimensions by taking an uninflated balloon and marking some dots on it. Now, inflate the balloon. Every dot gets farther away from every other dot. Our universe works the same way in three dimensions.
So, that brings up the question---if our Universe is expanding, what is it expanding into?
2) Outside our Universe: The cheap answer is that we can never know, since by definition it is beyond our universe. That's the best answer we can currently give, based on observations and generally-accepted theory.
There is no 'edge' to our Universe; even if you were able to somehow able to travel faster than light, and go beyond our observable universe, you would never encounter an edge, no matter how far you looked. Likewise, the Earth is finite in size, but there is no edge to the Earth; it's a curved surface. Mathematicians would call this a 2-dimensional surface of positive curvature, embedded in 3 dimensions---you can travel around the earth, and eventually end up where you start. The universe works the same way, except that it is a three-dimensional curved surface embedded in four (spatial) dimensions. Just like we can't find the center of the Earth anywhere on its surface, there is no center to the Universe that we can find, because we are stuck on its 3-dimensional surface; the center is in a higher dimension. (I know that sounds bizarre!)
Incidentally, current observations show that our universe has negative curvature, the opposite of a sphere; (it will expand forever, and you could never travel in one direction and end up where you began like you can on surfaces of positive curvature such as the Earth).
As for what the fourth spatial dimension is that we can't observe because it is OUTSIDE OUR 3-D Universe, it is beyond what current science can answer. Read the numerous other answers to this question below for other peoples' thoughts on this.
How would we know? Are we ever GOING TO GET THERE? Well, build a time machine and go into the future so we can see if we will, but we can't do that right now.
- In actuality, the Universe is an ellipsoid (3 dimensional oval) in which as someone else stated, you always seem to be at the center due to the vastness and gravitational forces. In theory, the end of the universe (if possible to reach) would be impossible to see because light bends as it hits the end, so if you could see far enough (provided noting impairs your sight) you would be looking at the back of yourself. Outside of our universe is many other universes which (may) be reached by use of black holes. What these universes are suspended in is unknown, the most likely answer being infinite nothingness.
- It would be everything else other than the singularity that became the physical universe as we know it just before the big bang.
- There is a theory that "on the other side of the universe" there is another universe. However, it's not a popular theory.
- There are several theories. Some hypothesize that the universe is ever-expanding and infinite. However, that raises some questions. What is the universe expanding into? What is in the emptiness the universe is not yet occupying? Will we ever hit a wall? It is safe to say that if the universe ever did hit a wall, it would not affect earth, or even our galaxy. Einstein theorized that it is possible that there are two universe, connected by a wormhole. Others say that the 'big bang' that created us was a 'splat' from another, older, parallel universe that was having a violent episode. The material from that 'splat' surged into emptiness, so much so that it created an alternate continuum, and then exploded as a huge white hole, creating our universe. They also say it's been expanding since then. Some experts, as Steven Hawking, believe that all the matter in the universe was at one time compacted into something small, the size of a marble maybe. It was incredibly massive or perhaps more accurately, incredibly energetic. It is currently believed that there were no actual physical particles present. It had an explosive reaction to something, and bang--hello universe. There's much more, of course, but this is already a long answer.
- The universe, according to Einstein, is circular. All of space and matter is observably distorted or warped by gravitational fields, and all of the universe is encompassed in one gigantic gravitational field. If the universe is indeed closed, then if you traveled in any direction in a straight line you would (assuming you didn't run into a planet or black hole or something) eventually come back to the same exact spot. This concept is the basis for the hoaky but interesting movie "the paycheck" with Ben Affleck.
- According to the newly emerging "Membrane" Theory, or Brane Theory, the universe as we know it is really a membrane, or flexible bumpy plane (or so it would seem to the quantum elves who can see things in the 11 dimensions theorized to be necessary for certain things to occur). Our membrane is one of perhaps countless membranes. They are all around us, everywhere. "Closer to us than our skin", as one physicist remarks. When 2 membranes collide, the result is... a new universe. Black holes may be evidence that such a collision has happened.
- Maybe the universe is whatever we want to think it is. I think that no human will ever really know, and heck, maybe nothing's real. Yet again, no one really knows.
- We can't see any edge of the universe. It might be infinite, in which case it has no center and no "other side". So astronomers often talk about the "observable universe". This is because it's not possible to see things more than a certain distance away, because the time it would have taken the light to get here is longer than the age of the universe. But if you change the question to ask about the observable universe then it still doesn't make sense, because we're at the center of the observable universe. (Think about it.) If you ask "what is at the furthest reaches of the observable universe" then the answer is that as far as we can tell it's pretty much the same everywhere (on a large scale). Every part of the universe has galaxies of various shapes and sizes.
- There must be something beyond our universe that is different from space-time as we know it. We all know about the big bang theory that suggests that space-time was created between 10 and 20 billions of years ago. Hence, space-time is absent outside the universe since the big-bang didn't create the 'area' outside our universe. However, we can't conclude that there is nothing there. So, we can say that there is something other than space-time present. Perhaps it is emptiness. Who knows?
These things are so enjoyable to ponder. We are so locked in to our amazingly tiny view of the universe relative to both space and time that we are surely not yet open to some Very Big Ideas that will 'change' everything. At one time, intelligent thinking people could not fathom the idea that the earth is a globe moving in an orbit around the sun. People once considered it obvious and common-place that animals sprang whole from various kinds of plants. Surgeons didn't hesitate (it was a brutal business back then) to cut into people without even a simple soap and water wash of their hands, or of their instruments. Even into the 20th century, some were convinced that travel to the moon and other bodies in space was absolutely and fundamentally impossible-- not because of technology but because of natural unbreakable limits and laws. People are just now 'getting' that time is relative.
Regarding the 'edges' of space, people are probably right who argue that no matter where you are you will appear to be in the center. One of those Very Big Ideas (that I make no claim to understand) is that the 'border' of space is itself three-dimensional, and therefore not reachable in anything like a conventional sense. We move in three dimensions, so there is no place we can go, and find ourselves in something other than a three-dimensional space. There is really nothing 'beyond', unless you break through the tiny theorized dimensions locked fast in the mysterious quantum. Even then, anyplace else that could possibly exist would not be 'outside' of our universe but parallel to it.
We haven't even mentioned the possibility (there is evidence in support of this) that space itself is expanding, and this may in part account for the redshift in our observations of distant galaxies.
- One could say that we are on the other side of the universe. There truly is no "Wall" per say in the universe. The universe is a curve. If one follows the curve, one will eventually end up exactly where one started.
- I do have a hypothesis about the universe "looking" like its spreading, If the Earth orbits the Sun and the Sun orbits the center of the galaxy, maybe all galaxies orbit something even bigger. which would make it look like it was spreading but really has the effect of a horse race. (they start at the same place but the slower horses gets left behind and the fast ones get farther from the others) so it would be thinning instead if spreading.